Phononic thermal Hall effect in diluted terbium oxides

We observe thermal Hall conductivity for (Tb0.3Y0.7)2Ti2O7, which is even larger than the previously observed thermal Hall conductivity for Tb2Ti2O7 [Science 348, 106 (2015)10.1126/science.1257340]. The robustness against the dilution of the Tb magnetic moment indicates the Hall effect of phonons is the origin of thermal Hall conductivity in Tb pyrochlore oxide. The temperature and magnetic field dependences are observed to follow the empirical relation that the Hall angle is proportional to the magnetization. We also investigate thermal Hall conductivity for (Tb0.3Y0.7)3Ga5O12. We observe barely finite thermal conductivity at low temperatures. This confirms the thermal Hall conductivity in Tb-garnet oxide. The origins of the empirical relation in the pyrochlore system and the magnitude difference between the two systems are discussed comparatively with previously proposed theories of the phonon Hall effect.